What is the pH of 115 mL of a 1.50 m solution of HNO2 that is titrated with a 1.50 M solution of LiOH at the equivelence point?

To find the pH of a solution at the equivalence point of a titration, you need to understand the nature of the reaction occurring between the two solutions. In this case, the reaction is between a strong base (LiOH) and a weak acid (HNO2). To determine the pH at the equivalence point, you need to first calculate the moles of each reactant.

Step 1: Calculate the moles of HNO2 in the solution.
- You are given the volume of the solution (115 mL) and the molarity (1.50 M). To calculate the moles, use the formula:
Moles = Volume (in L) x Molarity
Convert the volume to liters:
Volume = 115 mL / 1000 mL/L = 0.115 L
Moles of HNO2 = 0.115 L x 1.50 M = 0.173 moles

Step 2: Determine the stoichiometry of the reaction.
- The balanced equation for the reaction is as follows:
HNO2 + LiOH → LiNO2 + H2O
From the equation, you can see that 1 mole of HNO2 reacts with 1 mole of LiOH to produce 1 mole of water.

Step 3: Calculate the moles of LiOH required for complete reaction.
- Since the stoichiometry of the reaction is 1:1, the moles of LiOH needed will be equal to the moles of HNO2.
- Moles of LiOH = Moles of HNO2 = 0.173 moles

Step 4: Calculate the concentration of LiOH at the equivalence point.
- The volume of LiOH solution used at the equivalence point is not provided, so we cannot calculate the exact concentration. However, we know that the molarity of the LiOH solution is 1.50 M, which means 1 liter of the solution contains 1.50 moles of LiOH.

Step 5: Calculate the volume of LiOH solution used to reach the equivalence point.
- Since the moles of LiOH and the concentration of LiOH solution at the equivalence point are the same, we can use the formula:
Moles = Volume (in L) x Molarity
- Rearranging the formula, we can determine the volume of LiOH solution used:
Volume = Moles / Molarity
Volume = 0.173 moles / 1.50 M = 0.115 L = 115 mL

Step 6: The pH of the solution at the equivalence point.
- At the equivalence point, the stoichiometric amount of acid has reacted with the stoichiometric amount of base. Therefore, the solution consists only of the salt (LiNO2) and water (H2O).
- Since the salt LiNO2 is a strong electrolyte, it dissociates completely into Li+ and NO2-.
- The water does not contribute to the pH, as it is neutral.
- The pH of a solution containing only LiNO2 is determined by the hydrolysis of the anion (NO2-).
- NO2- is a basic anion and will react with water as follows:
NO2- + H2O → HNO2 + OH-
Since the reaction produces OH-, the solution will be basic.
- To find the pH of a basic solution, you need to calculate the pOH and then convert it to pH using the formula pH + pOH = 14.

Let's calculate the pOH:
- First, calculate the moles of NO2-: Since there is a 1:1 stoichiometry between LiNO2 and NO2-, the moles of NO2- will also be 0.173 moles.
- Next, calculate the concentration of NO2-: Since the volume of the solution is 115 mL (0.115 L), the concentration of NO2- can be calculated as follows:
Concentration = Moles / Volume
Concentration = 0.173 moles / 0.115 L = 1.505 M
- Now, calculate the pOH using the concentration of NO2-:
pOH = -log[NO2-] = -log(1.505) = 0.824

Finally, calculate the pH using the pOH:
- pH + pOH = 14
- pH = 14 - pOH = 14 - 0.824 = 13.176

Therefore, the pH of the solution at the equivalence point is approximately 13.176.